Báo cáo toán học: "Degree Sequences of F -Free Graphs" ppsx

... x. For example, for f : x → x 2 we have e f (F )=e (F ); thus e f (F ) can be viewed as a generalization of the size of F . Define ex f (n, F ) to be the maximal value of e f (G)overallF -free ... rate of growth of f. For example, if f grows so fast that e f (G) is dominated by the contribution from the vertices of degree n − 1, then the conclusion of T...

Ngày tải lên: 07/08/2014, 13:21

... one-twin-free and connected. Proof. In this proof, we use twin, twin-free and terminal for one-twin, one-twin-free and one-terminal, respectively. By Corollary 7, we know that G is not terminal. If ... the concatenation of the part of P ∗ going from v 1 to v k and the part of P r+1 going from v k to x. The length of P is greater than or equal to q + r + 1: there are q edges from v 1 t...

Ngày tải lên: 07/08/2014, 15:22

... 92E10 Abstract For graphs F and G an F -matching in G is a subgraph of G consisting of pairwise vertex disjoint copies of F . The number of F -match ings in G is denoted by s (F, G). We show that for every ... if there is one. In fact, this number is the product of the number of F -ma t chings in every connected component of the forest. By our construction of Z, at l...

Ngày tải lên: 08/08/2014, 12:23

Ngày tải lên: 05/08/2014, 09:46

... in the other copy of G. The following lemma, from [1], relates the hamitonicity of prisms and squares for the electronic journal of combinatorics 2 (1995), #R5 4 Proof: Our proof is by induction ... subgraph of AO(G) × e,namelythat subgraph induced by all extensions of Γ. We observe that H can be partitioned into • [positive pairs] edges of the form [+Γ, +Γ  ], and • [mates] edge...

Ngày tải lên: 07/08/2014, 06:20

... The following lemma will be used to determine the number of common neighbors of a pair of vertices in X n . Lemma 5. For integers n, s, n ≥ 2, denote by F n (s) the number of solutions of the congruence x ... journal of combinatorics 14 (2007), #R45 7 2. The multiplicity of zero as an eigenvalue of X n is n − m. 3. If α(λ) is the multiplicity of the eigenvalue λ of X n ,...

Ngày tải lên: 07/08/2014, 15:22

... i G N (U). As a u 0 -faulty set is by definition finite, there is therefore no such set. Second, let f 1 , f 2 , . . . be an enumeration of the edges of G 0 . Denote the endvertices of f 1 by x and y, ... satisfy (a)–(c). However, if we agree that v n is a neighbour of itself if there is a loop at v n then what follows covers also loops. For each neighbour w of v n in G n−1 for...

Ngày tải lên: 07/08/2014, 21:20

... choice of a special element of highest order among the 7 different expressions of S 1 has the advantage of enhancing the computing efficiency of the clique number of G n (A i ). 3 The computation of ... Science Fund of Guangdong Province (04010384), the Science Fund of Guangxi Province (0991074, 0991278), the Research Fund of Guangxi Education Committee (200911LX433), the Res...

Ngày tải lên: 08/08/2014, 11:20

... n i f i = f i , so F i = f i + f i+1 + f i+2  s since f i+1 , f i+2 are non- positive. If F i = s then f i = s and so, by s  n i−1 f i−1 + n i f i we conclude that f i−1  0. Also f i+1 = f i+2 = ... inequalities s  3f i + f i+1 and s  f i+1 + 2f i+2 . If f i+2  2f i , then the first inequality leads to s  f i + f i+1 + f i+2 . Otherwise 2 f...

Ngày tải lên: 08/08/2014, 12:23

... of ∆, together with a collection o f subsets F ⊆ 2 V such that F ∈ F, G ⊆ F ⇒ G ∈ F, called the faces of ∆. For technical purposes, we include the emptyset as a face. Lov´asz’s original proof ... vertices for the first of these nodes induce as a subgraph of E 2n+2 a copy of EL n−5 while for the second of these nodes the remaining vertices induce a s a subgraph of E 2n+...

Ngày tải lên: 08/08/2014, 14:23